Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524071 | C2 | semidirect |
| 2. #16863974 | C2 | semidirect |
| 3. #16863960 | C2 | semidirect |
| 4. #16863649 | C2 | semidirect |
| 5. #16863642 | C2 | semidirect |
| 6. #16863632 | C2 | semidirect |
| 7. #16863625 | C2 | semidirect |
| 8. #16863438 | C2 | semidirect |
| 9. #16863393 | C2 | semidirect |
| 10. C2×#14523965 | C2 | semidirect |
| 11. C2×#131×C67 | C2 | semidirect |
| 19. #14524022 | C22 | semidirect |
| 23. #14524017 | C22 | semidirect |
| 29. #14523977 | C22 | semidirect |
| 30. #14523975 | C22 | semidirect |
| 31. #14523968 | C22 | semidirect |
| 32. #14523968 | C22 | semidirect |
| 35. #14523965 | C22 | semidirect |
| 36. #14523965 | C22 | semidirect |
| 40. C2×M16×C67 | C22 | semidirect |
| 42. C22×C8×C67 | C22 | semidirect |
| 79. M16×C67 | D4 | semidirect |
| 152. C67 | #3062 | semidirect |
| 154. C2×#131 | D67 | semidirect |
| 172. C2×M16 | C2×D67 | semidirect |
| 174. C22×C8 | C2×D67 | semidirect |
| 220. M16 | C22⋊D67 | semidirect |